Start cranking the wheel and turn the adjusting barrel to the left while counting the turns until the chain jumps to the next cog.

Once the chain has jumped to to the next cog, shift all the way down to the smallest cog. Turn the adjusting barrel all the way to the right.

Then turn the adjusting barrel 1/2 the number of turns, counter clock wise, you counted (for example, if it took 4 turns for the chain to jump to the next cog, then you turn it 2 turns).

You should now be able to shift gears without hesitation. If you see that there’s a little hesitation, adjust the barrel slightly, taking half turns counter clock wise until you are satisfied with the shifting.

this sounds pretty straight forward, which is great, however I’m having some trouble with one important element: my barrel adjuster won’t turn. the one for my front derailleur will turn if given enough slack in the cable, but the one for the rear refuses to budge. Any suggestions?